The A380 has a total waste tank capacity of 2096L or 554 US gal, according to Airbus.
B. Capacity
There are four waste tanks, two upper deck tanks and two main deck tanks, see FIGURE
5-4-10-991-003-A.
(1) Upper Deck Waste-Tanks
- 373 l (99 US gal).
Each tank is precharged with 35 l (9 US gal) of chemical fluid.
(2) Main Deck Waste-Tanks
- 675 l (178 US gal).
Each tank is precharged with 35 l (9 US gal) of chemical fluid.
(3) Total Waste Tank Capacity
- 2096 l (554 US gal).
The size will vary for each aircraft type, the Boeing 747 had a capacity of only 1000L.
Smaller General Aviation aircraft do not have lavatories, this depends on aircraft size and purpose. The average Cessna will not have lavatories either, pilots have to plan their stops properly or rely on accessory such as the TravelJohn. Larger General Aviation aircraft such as smaller jets and aircraft designed for more than 4 passengers are more likely to have lavatories on board.

(Image Source: Siebert Aero)
There is no dumping system for waste tanks, mostly for hygienic and environmental reasons, as the waste tanks are not only filled with fecal and thus biological matter, but also with chemicals.